1. Field of the Disclosure
The field of the disclosure is that of communications networks. More specifically, the disclosure can be applied in the context of a communications network in which each data packet coming from a source node is encoded, for example with an LDPC (low density parity check) type encoding, i.e. a code for which the parity check matrix is of low density), and is then decoded by a destination node.
2. Related Art
Here below in this document, the disclosure will focus more particularly on a description of the problems and issues existing in the decoding of source data packets encoded according to an LDPC type encoding in a meshed communications network, which the inventors of the present patent application have had to cope with. Naturally, the disclosure is not limited to this particular field of application.
FIG. 1 is a schematic illustration of a wireless meshed network formed by a source node 101, several relay nodes (101, 102, 103, 104, 105) and a destination node 106.
Clearly, a meshed network of this kind may comprise several source nodes 101 and several destination nodes 106.
The description here below will be situated by way of an illustrative example in a case where the data packets sent out by the source node 101 are encoded source packets b1 and b2 resulting from an LDPC type channel encoding.
In FIG. 1, the encoded source packets b1 and b2 are relayed by the relay nodes 101 to 105.
Classically, the encoded source packets b1 and b2 may be either relayed as such (i.e. without combination with other data packets), as is the case with the relay nodes 102 and 103 in the example of FIG. 1, or combined with other data packets as is the case for example with the relay nodes 104 and 105 in the example of FIG. 1.
A relay node may therefore:                either combine data packets received at input and then transmit a combined data packet, for example a linear combination of the data packets received at input. This case, the relay node is called a “combinant relay node”;        or simply relay data packets received at input without creating a combination between data packets. In this case, the relay node is called a “non-combinant relay node”.        
It must be noted that a packet received at input of a relay node may be either an encoded source packet (b1 or b2) or a linear combination of encoded source packets.
In the example of FIG. 1, the destination node 106 receives four packets:                two packets y1 and y2 not combined by the non-combinant relay nodes 102 and 103 respectively, and        two combined packets Pc and Pc′, each resulting from a same linear combination of the encoded source packets b1 and b2. This linear combination (b1+b2) is made by the combinant relay node 104 for the combined packet Pc and by the combinant relay node 105 for the combined packet Pc′).        
A description shall now be given of a prior art technique currently used in the above-mentioned context, i.e. a meshed network comprising a destination node which must perform a decoding on the basis of several received packets, for which certain packets (known as combined packets) result from a same linear combination.
Once the set of data packets has been received at its input, the destination node 106 applies an LDPC decoding to each data packet received. Each decoding is done with a parity check matrix for the LDPC decoding on an input vector formed by the four received packets: y1, y2, Pc and Pc′.
If the LDPC decoding converges towards a correct solution, the destination node retrieves the originally sent source data packets.
Such a convergence of an LDPC decoding is obtained when the rows and the columns of the decoding parity check matrix built at the destination node 106 are mutually independent, i.e. when the parity check matrix has no cycles. Indeed, these cycles are present when the rows or columns of the parity matrix have a certain correlation or resemblance with one another.
The cycles in question are determined from a representation in the form of a graph of an LDPC parity matrix. These graphs link the nodes of variables (which correspond to the bits of each LDPC code word) and parity variables (which correspond to the parity bits in an LDPC code word)
A cycle in a graph is a path on the graph that makes it possible to go out from a node and return to this same node without passing through the same branch. The size of a cycle is given by the number of branches contained within the cycle. The size of the shortest cycle is called a “girth”. The presence of cycles in the graph impairs decoding performance because of a phenomenon of self-confirmation during the decoding.
Now, when the decoding is done from received packets which result from a same linear combination, this inevitably leads to a correlation between the rows of the parity matrix, even in the event of different errors present in each of the packets. Different errors may affect the combined packets when these packets are transmitted through different channels to the destination node.
This is the case for example in FIG. 1 where the combined packets Pc and Pc′ come from a same basic combination and are therefore mutually correlated. The rows of the decoding matrix are therefore not independent of one another.
Thus, for a meshed network, the classic LDPC decoding using a parity matrix is not optimal owing to the presence of these repetitions of messages within the communications network.